Since \(\nu \sim C^{+}(0,1)\) , Step 2 above can be easily accomplished by introducing an auxiliary parameter \(W\)  such that \(\nu ^2 \mid W \sim \mbox{IG}(1/2, 1/W)\)  and \(W \sim \mbox{IG}(1/2, 1)\)  [1]} and then obtaining conditionally conjugate inverse-gamma updates for both \(\nu ^2\)  and \(W\) . We now repeat the above steps for a large number of iterations and discard a burn-in to obtain posterior samples of the unknown parameters.
